Can bones in IK chains be also moved independently?
If I get you correctly, sure.  You just add another bone:

In your particular case, you would:

Duplicate bone 3 and delete any constraints from this duplicate.
Parent this duplicate to bone 3.
Disable deform on bone 3, and rename any vertex groups on the mesh to follow the duplicate instead (&quot;3.001&quot; likely.)

That way, bone 3 still takes place in the IK chain, and you have a deforming bone that defaults to the orientation of 3, but is still independently manipulable.
Should be said, even though you can do that, it doesn't mean you should do that.  How most people would approach the situation in your picture is to make 2 the IK bone, move the rest pose of 4 to the rest pose tail of 2, decrement the chain length by 1, and then give 3 a world-&gt;world copy rotation constraint targeting 4.  (An alternative here is to enable rotation on the IK constraint, but that's less reliable-- the IK solver doesn't do well with rotation enabled.)